How do I prevent hair flickering in Cycles?
It could be your UV coordinates, which are "generated". Since they are probably calculated in world coordinates, moving the object also moves the UV coordinates. It could cause shimmering "noise".

I don't think your node set up is what you want really. You should use the hair BSDF shader. Put 2 nodes using hair BSDF, one for reflection (hair color), and one for transmission (hair translucency). Mix between them and you are done. Consider creating manual UV coordinates and not using generated ones.

Good luck!